Are you sure you don't have it already? Like, when you go to the "Vrandtic Folklore" tab under miner, does it say "You have not read the relevant folkore" or does it just say "No items"? There are no folklore items yet that use the folklore book for the second mining tab, so if you're only looking there you won't see anything and it will say "No Items" even if you have the book.

If it does say you haven't read the book yet, double check your inventories even if you thnk a search is saying you don't have it. Check you chocobo saddlebag and each of your retainers. Is it possible the book was on a retainer that you have since stopped paying for?